If you see 'DRAFT' besides your email campaign - this email campaign will still have been sent out as you will see the Sent information is populated and a report bar chart icon to see the results - As shown below in red: 

The Draft only refers to the fact that the email campaign when created is set up as a draft by default.

If you open up the campaign you will see a checkbox called 'Draft' with a check set as default:

Just un-check the box to remove 'DRAFT' from the campaigns list.